Client adoption isn't a problem any more, IE is declining to around 30% on most popular sites. The largest issue with killing flash is the legacy: video players, games, even carousels use it.
If omegle was released in the next months, it likely wouldn't use flash.
Fibs. The whole reason I'm using flash in my startup (and it is a major component atm) is because of IE share (and the relative immaturity of HTML5). Are you really telling me that you want to deny your service to a fresh install of windows?
While many people appreciate the benefit of better browsers there is still a significant portion that don't and hopping aboard this wagon prior to full adoption means that you exclude them or present roadblocks to them.
I have the added benefit of targeting (in part) the older generation with the software I produce making all this excitement muted without cross-browser consensus.
I think it depends strongly on your target market. If you're building B2B enterprise software used exclusively on PCs on a desk, in an office, with no remote access, the mobile might be less important.
also, the sort of enterprise you speak of would certainly not be purchasing software like these - they'd stick with the trusted and known big name vendors. As they say, nobody ever got fired for using IBM (or microsoft).
It's still a tricky choice though. By going with Flash you're tying yourself into a dying technology which may not be such a hot choice if you're building a business [1]
I'd still try to go with js/html and shim away as best I could for older IEs.
I work for a company whose target audience tends to be men over 65 years old... And we've seen mobile devices (specifically tablets) grow to nearly 17% of our traffic in the past two years.. I'd say mobile is critical, even more for seniors.
If omegle was released in the next months, it likely wouldn't use flash.